1. Field of the Invention
The present invention relates generally to an apparatus and method for a multiuser receiver using a linear Minimum Mean Square Error (MMSE) scheme in a Code Division Multiple Access (CDMA) communication system. More particularly, the present invention relates to an apparatus and method for a multiuser receiver using an MMSE scheme, capable of improving a Bit Error Rate (BER) performance.
2. Description of the Related Art
A multiuser detection is a receiving scheme to detect a desired user signal, while mitigating the multiple access interference (MAI), noise and near far effect, in a wireless communication system where multiple users exist. Among the multiuser detection schemes for asynchronous Direct-Sequence Code Division Multiple Access (DS-CDMA), a Maximum Likelihood Sequence Detector (MLSD) achieves the best bit error rate (BER) performance. However, because the BER exponentially increases as the number of users increases, the MLSD is difficult to implement when there are many users. To solve this problem, suboptimum receivers have been proposed. One type of suboptimum receiver is a linear multiuser receiver using a Minimum Mean Square Error (hereinafter, referred to as MMSE) scheme. The multiuser receiver includes a conventional matched filter (CMF) and an MMSE filter. However, in the asynchronous DS-CDMA, the performance of the CMF is degraded when the number of users increases. Also, when the CMF is applied to the asynchronous DS-CDMA having the near far effect, its performance is degraded. For example, in the environment where the near far effect is serious or in the fading channel environment, the degradation of the performance becomes more serious when the magnitude of the received signal is small.
Hereinafter, a description will be made on an MMSE receiver using the CMF in an asynchronous DS-CDMA where the number of users is K and the bandwidth is restricted within a slow fading channel.
Equation (1) represents a signal r(t) received by a base station in a baseband for time t(−∞<t<∞).
                              r          ⁡                      (            t            )                          =                                            ∑                              k                =                0                            K                        ⁢                          S                              k                ⁡                                  (                  t                  )                                                              +                      n            ⁡                          (              t              )                                                          (        1        )            where Sk(t) denotes a received signal of a kth user at time t, and n(t) denotes an Additive White Gaussian Noise (AWGN) at time t.
When the number of users is K, binary data signals of the respective users are multiplied by unique spreading signals and are then transmitted. The received signal Sk(t) of the kth user is expressed as Equation (2):
                              S                      k            ⁡                          (              t              )                                      =                                            P              k                                ⁢                      R            k                    ⁢                      ⅇ                          jθ              k                                ⁢                                    ∑                              i                =                                  -                  ∞                                            ∞                        ⁢                                          b                i                                  (                  k                  )                                            ⁢                                                a                  i                                      (                    k                    )                                                  ⁡                                  (                                      t                    -                                          τ                      k                                        -                                          iT                      b                                                        )                                                                                        (        2        )            where k is the total number of users, Pk is a signal power transmitted from the kth user, Rk is a fading amplitude of the kth user, bi(k) is a symbol transmitted from the kth user at an ith sampling interval, Tb is a transmitted symbol period, θk is a phase angle of the kth user with respect to a 0th user, τk is a timing offset of the kth user with respect to a 0th user, bi(k) is an ith bit of a kth user and satisfies the condition of bi(k)ε[+1, −1], and ai(k)(t) is a spreading signal for the bit bi(k) of the kth user at time t.
The spreading signal ai(k)(t) for the bit bi(k) of the kth user is expressed as Equation (3):
                                          a            i                          (              k              )                                ⁡                      (            t            )                          =                              ∑                          n              =              1                        N                    ⁢                                    c                              n                +                iN                            k                        ⁢                          q              ⁡                              (                                  t                  -                                      nT                    c                                                  )                                                                        (        3        )            where cn(k) is an nth chip of a kth user PN sequence, ak is a kth user spreading sequence and ak=(c1, . . . , cN)T.
If ak is a random spreading sequence, cn(k) may have a value between [+1, −1]. N is a processing gain and is expressed as Tn/Tc. Rk is a fading amplitude of the kth user and follows a Rayleigh distribution. Rk is expressed as Equation (4)
                                          f                          R              k                                ⁡                      (            r            )                          =                              2            Ω                    ⁢          r          ⁢                                          ⁢                      exp            ⁡                          (                              -                                                      r                    2                                    Ω                                            )                                                          (        4        )            
In Equation (4), E|Rk2|=Ω, and Ω is a second moment of the fading gain. The random variable sets {τk}, {bi(k)} and {Rk} are mutually independent. Elements of the respective sets are independently and identically distributed.
In modem digital communication systems, digital data symbols are transmitted in a continuous pulse form with a characteristic suitable for channel transmission. When specific binary data is to be transmitted to a remote receiver, a data signal must be loaded on an appropriate carrier frequency and different pulses must be allocated to basic digital symbols “0” and “1”.
In this procedure, a pulse shaping filter increases a bandwidth efficiency, minimizes an intersymbol interference, and maintains a signal to noise ratio (SNR).
In the receiver, a basic pulse q(t) must satisfy the condition of Equation (5):
                                          ∫                          -              ∞                        ∞                    ⁢                                                    q                2                            ⁡                              (                t                )                                      ⁢                          ⅆ              t                                      =                  T          c                                    (        5        )            
In Equation (5), q(t) is a square wave comprising a value of “1” in the interval [0, Tc] and “0” outside the interval [0, Tc], and satisfies the condition of Equation (5).
The pulse shaping filter reduces the noise effect at the receiver and the interference with other signals at the adjacent channels. A pulse shaping filter in FIG. 1 is a spectrum raised cosine pulse shape made considering a Nyquist pulse shaping. The raised cosine spectrum is expressed as Equation (6):
                                          H            RC                    ⁡                      (            f            )                          =                  {                                                                      T                  c                                                                              0                  ≤                                                          f                                                        ≤                                                            1                      -                      β                                                              2                      ⁢                                              T                        c                                                                                                                                                                                                            T                      c                                        2                                    ⁢                                      {                                          1                      +                                              cos                        ⁢                                                  {                                                                                                                    π                                ⁢                                                                                                                                  ⁢                                                                  T                                  c                                                                                            β                                                        ⁢                                                          {                                                                                                                                  f                                                                                                  -                                                                                                      1                                    -                                    β                                                                                                        T                                    c                                                                                                                              }                                                                                }                                                                                      }                                                                                                                                          1                      -                      β                                                              2                      ⁢                                              T                        c                                                                              ≤                                                          f                                                        ≤                                                            1                      +                      β                                                              2                      ⁢                                              T                        c                                                                                                                                                0                                                                                                      f                                                        ≥                                                            1                      -                      β                                                              2                      ⁢                                              T                        c                                                                                                                                                    (        6        )            
The raised cosine spectrum of Equation (6) is expressed as Equation (7) in time domain:
                              g          ⁡                      (            t            )                          =                                            sin              ⁡                              (                                                      π                    ⁢                                                                                  ⁢                    t                                                        T                    c                                                  )                                      ⁢                          cos              ⁡                              (                                                      πβ                    ⁢                                                                                  ⁢                    t                                                        T                    c                                                  )                                                                                        π                ⁢                                                                  ⁢                t                                            T                c                                      ⁢                          (                              1                -                                                      4                    ⁢                                          β                                              2                        ⁢                                                  t                          2                                                                                                                          T                    c                    2                                                              )                                                          (        7        )            where β is an excess bandwidth and is a value exceeding Nyquist minimum bandwidth.
FIG. 1 is a block diagram of a multiuser receiver using a CMF in a conventional asynchronous DS-CDMA communication system.
Referring to FIG. 1, the multiuser receiver includes an antenna 100, a matched filter unit 110 comprising (K+1) number of CMFs, and an MMSE filter 120.
The CMFs of the matched filter unit 110 are analogous to those described in Equations (6) and (7).
In the CMF, a jth sample r0[j] of a first user output passing through a pulse shaping is expressed as Equation (8):
                                          r            0                    ⁡                      [            j            ]                          =                              ∫                          -              ∞                        ∞                    ⁢                                    r              ⁡                              (                                                      jT                    c                                    -                  U                                )                                      ⁢                          q              ⁡                              (                                  -                  u                                )                                      ⁢                          ⅆ              u                                                          (        8        )            
If a timing offset of the first user is zero and a detection process is based on a single symbol interval [0, Tb], Equation (8) may be rewritten as Equation (9):
                                          r            0                    ⁡                      [            j            ]                          =                                                            P                0                                      ⁢                          R              0                        ⁢                          T              c                        ⁢                          b              0                              (                0                )                                      ⁢                          c              j              0                                +                                    ∑                              k                =                1                            K                        ⁢                                                            P                  k                                            ⁢                              R                k                            ⁢                              T                c                            ⁢                                                ∑                                      -                    ∞                                    ∞                                ⁢                                                      ∑                                          n                      =                      1                                        N                                    ⁢                                                            b                      i                                              (                        k                        )                                                              ⁢                                          c                                              n                        +                        iN                                            K                                        ⁢                                          g                      ⁡                                              (                                                                              jT                            c                                                    -                                                      τ                            k                                                    -                                                      iT                            b                                                    -                                                      nT                            c                                                                          )                                                                                                                          +                      η            ⁡                          [              j              ]                                                          (        9        )            
A spreading sequence ak of the first user is modulated by a symbol b0(1) transmitted for the interval [0, Tb]. Alternatively, the spreading sequence of the other users (k>1) is modulated by b−1(k) for 0≦t≦τk. Also, the spreading sequence is modulated by b0(k) for τk≦t≦Tc. The intersymbol interference from b−2(k) or b1(k) may exist depending on the value of τk. When tε[0, tb], vectors of the output signal samples passing through the CMFs are expressed as rT={r0[1], . . . , r0[N])T. The vector r is expressed as Equation (10):
                                          r            0                    ⁡                      [            j            ]                          =                                                            P                0                                      ⁢                          R              0                        ⁢                          T              c                        ⁢                          b              0                              (                0                )                                      ⁢                          a              0                                +                                    ∑                              k                =                1                            K                        ⁢                                                            P                  k                                            ⁢                              R                k                            ⁢                              T                c                            ⁢                                                ∑                                      i                    =                                          -                      2                                                        1                                ⁢                                                      b                    i                                          (                      k                      )                                                        ⁢                                      d                    i                                                                                +          η                                    (        10        )            where η is an Additive White Gaussian Noise vector. A jth element of the vector dj is expressed as Equation (11):
                              d          i          j                =                              ∑                          n              =              1                        N                    ⁢                                          ⁢                                    c                              n                +                iN                            k                        ⁢                          g              ⁡                              (                                                      jT                    c                                    +                                      τ                    k                                    -                                      iT                    b                                    -                                      nT                    c                                                  )                                                                        (        11        )            
A signal to noise ratio (SNR) is expressed as Equation (12):
                    SNR        =                                                            P                0                            ⁢                              ΩT                b                                                                    N                0                            ⁢                              T                b                                              =                                                    P                0                            ⁢              Ω                                      N              0                                                          (        12        )            
In addition, Equation (10) is expressed as Equation (13):
                              r          0                =                                            ∑                              j                =                1                            L                        ⁢                                                  ⁢                                          b                j                            ⁢                              P                j                                              +                      η            0                                              (        13        )            where bj is a data symbol, L may have a value between K and 3K−2, and Pj is a corresponding interference vector and is expressed as Equation (14):P1=√{square root over (P0)}R0a0  (14)
The MMSE filter 120 may have N number of coefficients because the interval is Tc. The output of the MMSE filter 120 is expressed as Equation (15), which corresponds to bit estimation value:{circumflex over (b0)}=sgn(CTr0)  (15)
The vector C is used for minimizing a Minimum Squared Error (MSE). The MSE is expressed as Equation (16):
                                                        MSE              =                            ⁢                              E                ⁡                                  [                                                            (                                                                                                    C                            T                                                    ⁢                                                      r                            0                                                                          -                                                  b                          0                                                                    )                                        2                                    ]                                                                                                        =                            ⁢                                                                    (                                                                                            C                          T                                                ⁢                                                  p                          1                                                                    -                      1                                        )                                    2                                +                                                      ∑                                          j                      =                      2                                        L                                    ⁢                                                                          ⁢                                                            (                                                                        C                          T                                                ⁢                                                  p                          j                                                                    )                                        2                                                  +                                                      C                    T                                    ⁢                  TC                                                                                        (        16        )            
If Equation (16) is differentiated with respect to C and the differentiated equation is equated with zero, the result is expressed as Equation (17):C=(A+p1p1T)−1P1  (17)
In Equation (17), “A” is given by Equation (18):
                    A        =                                            ∑                              j                -                2                            L                        ⁢                                                  ⁢                                          p                j                            ⁢                              p                j                T                                              +          T                                    (        18        )            
The signals of the respective users are detected through the above-described procedures. These procedures will now be summarized with reference to FIG. 2.
Referring to FIG. 2, in steps 200 and 202, when a base station receives signals through an antenna, it inputs the received user signals to the CMF 110. In step 204, the CMF performs the pulse shaping on the user signals. In step 206, the base station inputs the pulse-shaped samples to the MMSE filter 120. In step 208, the base station calculates bit estimation values of the respective users by using the samples. Then, the base station terminates the algorithm.
As described above, in the asynchronous DS-CDMA, the performance of the CMF is degraded when the number of users increases. The performance of the CMF is also degraded when the CMF is applied to the asynchronous DS-CDMA with the near far effect. For example, in the environment where the near far effect is serious or in the fading channel environment, the degradation of the performance becomes more serious when magnitude of the received signal is small.
Accordingly, there is a need for an improved system and method for multiuser detection using a linear MMSE scheme in an asynchronous DS-DCMA communication system, capable of improving a BER performance.